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Sierpinski/Riesel Base 5 Problem
This project is an extension of the original Sierpinski/Riesel problems (SoB/TRP). It is attempting to solve the Sierpinski/Riesel problems for base 5 by determining the smallest Sierpinski/Riesel numbers. Therefore, primes of the form k*5^n+/-1 are being sought for even k's. : Sierpinski Base 5 - The smallest even Sierpinski base 5 number is suggested to be k=159986. To prove this, it is sufficient to show that k*5^n+1 is prime for each even k < 159986. This has currently been achieved for all even k, with the exception of the following 40 values (as of 17 January 2014): :: k = 6436, 7528, 10918, 24032, 26798, 29914, 31712, 36412, 41738, 44348, 44738, 45748, 51208, 58642, 60394, 62698, 64258, 67612, 67748, 71492, 74632, 76724, 77072, 81556, 83936, 84284, 90056, 92158, 92906, 93484, 105464, 109208, 118568, 126134, 133778, 138514, 139196, 144052, 152588, 154222 : Riesel Base 5 - The smallest even Riesel base 5 number is suggested to be k=346802. To prove this, it is sufficient to show that k*5^n-1 is prime for each even k < 346802. This has currently been achieved for all even k, with the exception of the following 82 values (as of 25 April 2014): :: k = 3622, 4906, 22478, 23906, 26222, 35248, 35816, 52922, 53546, 63838, 64598, 66916, 68132, 71146, 76354, 81134, 88444, 92936, 100186, 102818, 102952, 109238, 109838, 109862, 127174, 131848, 134266, 136804, 138172, 143632, 145462, 145484, 146264, 146756, 147844, 151042, 152428, 154844, 159388, 164852, 170386, 170908, 171362, 177742, 180062, 182398, 187916, 189766, 190334, 194368, 195872, 201778, 204394, 206894, 207494, 213988, 231674, 238694, 239062, 239342, 246238, 248546, 259072, 265702, 267298, 271162, 273662, 285598, 285728, 296024, 298442, 301562, 304004, 306398, 313126, 318278, 322498, 325918, 325922, 327926, 335414, 338866 History Robert Smith originally presented the idea of a Sierpinski/Riesel base 5 search on 17 September 2004, in the primeform yahoo group. Using {3,7,13,31,601} as the covering set, he proposed that k=346802 is the smallest Riesel base 5 number. Shortly afterwards, Guido Smetrijns proposed that k=159986 is the smallest Sierpinski base 5 number. After doing most of the initial work himself, Robert posted in the mersenneforum.org on 28 September 2004, and thus, the distributed effort began. Other principle players in the development, management, and growth of the project are Lars Dausch, Geoff Reynolds, Anand S Nair, and Thomas Masser. During the first couple of years, the project remained very active. Both sieving and primality testing were handled through manual reservations in the Mersenne. On a side note, it is within this project that Geoffrey Reynolds created his srsieve to support the Sierpinski/Riesel problems. His initial post (27 Apr 2006) can be found here. Thus began his illustrious career in providing excellent sieving software for the prime finding community. His programs continue to be widely used by prime seekers today. His collaboration with Ken Brazier helped produce PPsieve, which revolutionized GPU sieving and established deeply sieved files for both Riesel and Proth prime forms. These files currently provide support for the Riesel Prime Search and Proth Prime Search projects. On 29 Aug 2006 the project officially launched its LLRNet. This provided for automatic distribution and primality testing of candidates. Manual reservations were continued on an individual basis. Participation continued to be healthy. However, over the next 4 years, interest waned. Interest remained low until March 2010 when a lively discussion took place to determine the project’s future. For the next few months, participation remained high. On 28 May 2010 manual reservations were ceased for primality testing and all remaining ranges were reserved for SR5’s LLRNet. Soon participation dropped again. In the fall of 2010, PrimeGird started reserving ranges to test in its PRPNet server. Testing among PrimeGrid users remained healthy. Finally, in December 2010, PrimeGrid hosted an end of year Mini Challenge on it’s PRPNet server benefiting the SR5 project. The last 10 days of 2010 (21 Dec - 31 Dec) was devoted to helping the Sierpinski/Riesel base 5 project remain active. The goal of the Challenge was to help the the SR5 project make 2010 the HIGHEST scoring year of the project in regards to primes found. The Mini Challenge was a huge success with PrimeGrid users finding 5 SR5 primes. Thus, on 7 January 2011, a collaboration was officially announced between SR5 and PrimeGrid. It remained in PrimeGrid’s PRPNet until 14 Jun 2013 when it was moved to BOINC. Primes found by PrimeGrid 326834*5^1634978-1 found by Scott Brown on 25 April 2014 | Official Announcement 207394*5^1612573-1 found by Honza Cholt on 9 April 2014 | Official Announcement 104944*5^1610735-1 found by Brian Smith on 9 April 2014 | Official Announcement 330286*5^1584399-1 found by Scott Brown on 21 March 2014 | Official Announcement 22934*5^1536762-1 found by Keishi Toda on 6 February 2014 | Official Announcement 178658*5^1525224-1 found by Keishi Toda on 31 January 2014 | Official Announcement 59912*5^1500861+1 found by Raymond Ottusch on 17 January 2014 | Official Announcement 37292*5^1487989+1 found by Stephen R Cilliers on 29 December 2013 | Official Announcement 173198*5^1457792-1 found by Motohiro Ohno on 4 December 2013 | Official Announcement 245114*5^1424104-1 found by David Yost on 1 November 2013 175124*5^1422646-1 found by David Yost on 31 October 2013 256612*5^1335485-1 found by Wolfgang Schwieger on 4 August 2013 268514*5^1292240-1 found by Raymond Schouten on 16 July 2013 243944*5^1258576-1 found by Tod Slakans on 5 July 2013 97366*5^1259955-1 found by Jörg Meili on 4 July 2013 84466*5^1215373-1 found by Raymond Schouten on 29 June 2013 150344*5^1205508-1 found by Randy Ready on 28 June 2013 1396*5^1146713-1 found by Randy Ready on 23 June 2013 17152*5^1131205-1 found by Bob Benson on 22 June 2013 92182*5^1135262+1 found by Randy Ready on 21 June 2013 329584*5^1122935-1 found by Stephen R Cilliers on 21 June 2013 305716*5^1093095-1 found by Randy Ready on 18 June 2013 130484*5^1080012-1 found by Randy Ready on 17 June 2013 97768*5^987383-1 found by Ulrich Hartel on 17 June 2013 55154*5^1063213+1 found by Senji Yamashita on 16 June 2013 243686*5^1036954-1 found by Katsumi Hirai on 16 June 2013 70082*5^936972-1 found by Scott Brown on 30 May 2013 102976*5^929801-1 found by David Yost on 9 May 2013 110488*5^917100+1 found by Ronny Willig on 25 March 2013 162434*5^856004-1 found by Predrag Kurtovic on 10 January 2013 174344*5^855138-1 found by Ronny Willig on 9 January 2013 57406*5^844253-1 found by David Yost on 7 November 2012 48764*5^831946-1 found by David Yost on 12 October 2012 162668*5^785748-1 found by Lennart Vogel on 3 July 2012 289184*5^770116-1 found by David Yost on 7 June 2012 11812*5^769343-1 found by Göran Schmidt on 2 June 2012 316594*5^766005-1 found by Michael Becker on 30 May 2012 340168*5^753789-1 found by Kimmo Myllyvirta on 18 May 2012 338948*5^743996-1 found by Ricky L Hubbard on 7 May 2012 18656*5^735326-1 found by Lennart Vogel on 3 May 2012 5374*5^723697-1 found by Kelvin Lewis on 13 April 2012 72532*5^708453-1 found by Göran Schmidt on 7 February 2012 2488*5^679769-1 found by Sascha Beat Dinkel on 24 November 2011 331882*5^674961-1 found by Ronny Willig on 11 November 2011 27994*5^645221-1 found by Philipp Bliedung on 18 July 2011 262172*5^643342-1 found by Kimmo Myllyvirta on 13 July 2011 49568*5^640900-1 found by Sascha Beat Dinkel on 1 July 2011 270748*5^614625-1 found by Puzzle Peter on 14 February 2011 266206*5^608649-1 found by Puzzle Peter on 10 February 2011 210092*5^618136-1 found by Puzzle Peter on 31 January 2011 301016*5^586858-1 found by Puzzle Peter on 24 January 2011 Primes found by SR5 since collaboration 109988*5^544269+1 found by ltd on 23 April 2011 68492*5^542553+1 found by ltd on 24 April 2011 Primes found by others 114986*5^1052966-1 found by Sergey Batalov on 3 June 2013 119878*5^1019645-1 found by Sergey Batalov on 3 June 2013